动态规划练习1--Unique Paths

题目内容

[引自] https://leetcode.com/problems/unique-paths/description/

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

How many possible unique paths are there?



Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

伪代码

核心: uniquePaths(i,j)=uniquePaths(i-1,j)+uniquePaths(i,j-1)
states数组保存状态值 states[i][j]表示到达i,j位置的不同路径数
边界值:初始边界为(0,x)和 (x,0)
初始化: states[0][0]=0,states[0][x]=0,states[x][0]=0
(1,1)表示初始位置,states[1][1]=0,states[1][2]=1,states[2][1]=1

算法

int uniquePaths(int m, int n)
int[][] states =new int[101][101]
states[1][1]=1
for  i=1 to m+1
for j=1 to n+1
if(i==1 and j==1)
continue;
states[i][j]=states[i-1][j]+states[i][j-1]
states[1][1]=0
return states[m]

java 代码实现

public int uniquePaths(int m, int n) {
int[][] states =new int[101][101];
states[1][1]=1;

for(int i=1;i<m+1;i++){
for(int j=1;j<n+1;j++){
if(i==1&&j==1){
continue;
}
states[i][j]=states[i-1][j]+states[i][j-1];
}
}
states[1][1]=0;
return states[m]
;
}